Chapter 13, Problem 35P

5. Represent the following system in state-space form. Write A, B, C and D clearly in your answer. d³y d²y dt3 - +5y=2u dt²

3. Find the transfer function H(s) and frequency response H (w) of the following system whose differential equation is given by d¹y d³y +3. dy +5 dt4 dt3 dt - d²u du 4y = - 5 dt² dt

1. Consider a plant that you want to control. The input u(t) and output y(t) of the plant are related by y(t) = 7 u(t) + w(t) where w(t) is an additive disturbance at the output which is bounded by -0.5 w(t) ≤0.5 for all time t. You want to build a controller so that the output follows a constant reference signal r(t) = where -15 ≤≤ 15. You will consider both open-loop and closed-loop for this problem. a) Sketch the block diagram of the plant. b) Please build an open-loop controller that sets the output to 7, assuming the disturbance is ignored. Please show your controller both as an equation and a block diagram. c) Say that you use the open-loop controller in part b, but now the disturbance w(t) is present. What is the maximum possible magnitude of error in the output for the reference signal? Suppose you have designed a feedback control for the plant where the controller has the form u(t) = K(r(t) − y(t)). Here K is the gain constant of the controller that you will design. d) Please…